IF Sn denote the sum of the first n terms of an AP and S2n =3Sn then S3n :Sn is e
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S2n=2n/2[2a+(2n-1)d]
Sn=n/2[2a+(n-1)d]
Also,3Sn=S2n
=>3.n/2[2a+(n-1)d]=2n/2[2a+(2n-1)d]
=>6a+3nd-3d=4a+4nd-2d
=>[2a=nd+d] ..(i)
S3n:Sn=3n/2[2a+(3n-1)d]:n/2[2a+(n-1)d]
=>S3n:Sn=3(nd+d+3nd-d):(nd+d+nd-d)
=>S3n:Sn=3(4nd):2nd=6:1
Hope it helps.
Sn=n/2[2a+(n-1)d]
Also,3Sn=S2n
=>3.n/2[2a+(n-1)d]=2n/2[2a+(2n-1)d]
=>6a+3nd-3d=4a+4nd-2d
=>[2a=nd+d] ..(i)
S3n:Sn=3n/2[2a+(3n-1)d]:n/2[2a+(n-1)d]
=>S3n:Sn=3(nd+d+3nd-d):(nd+d+nd-d)
=>S3n:Sn=3(4nd):2nd=6:1
Hope it helps.
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